Color system for matching and compounding colors



L. A. WISE Dec. 30, 1958 COLOR SYSTEM FOR MATCHING AND COMPOUNDING COLORS .WVE'VTOR.

Arromvey 2 Sheets-Sheet l Filed Dec.

GRAYING WITH BLACK COLOR SYSTEM FOR MATCHING AND COMPOUNDING COLORS Filed Dec. 16, 1955 2 Sheets-Sheet 2 NEUTRAL Q 3H+ZC SHADES H c a INVENTOR. \H +3c 4 BY MNEEE 74.1445

I y I I u COMPLEMENT 24% k I I GRAYING WITH THE commmsur rn ATTORNEY United States Patent COLOR SYSTEM FOR MATCHING AND COMPOUN DIN G COLORS Lambert A. Wise, Pittsburgh, Pa., assignor to Pittsburgh Plate Glass Company, a corporation of Pennsylvania Application December 16, 1955, Serial No. 553,552 7 Claims. (Cl. 35-283) This invention relates to a process of and means for selecting, matching and compounding colors in coating materials, inks and the like and it has particular relationship to a method of and means for matching and compounding colors in paints and inks which colors constitute shades, tints and values of a common hue.

In the compounding of colors in the preparation of coating compositions such as paints, varnishes, enamels and lacquers or, in the compounding of the colored inks, tinting and shading agents such as white and black pigments or a white pigment and a complement are often added to some hue such as a spectral hue selected from the well known color wheel which is based upon the primary colors of the spectrum and the secondary, tertiary and the like colors obtained by mixing these primary colors in various ways. In the selection, matching and compounding of colors, various arrangements have been made of chips of selected color upon a sheet member such as a sheet of paper or of cardboard. On such sheets the chips were commonly labeled so that the desired coating material could be selected and identified and the composition thereof determined for the convenience of the compounder. This method of selecting and formulating colors in coating compositions was not very satisfactory because the possible number of colors which can be identified by the human eye is quite large. It is even possible to arrive at a large number of different colors merely by adding to one given hue various amounts of a neutral tinting agent such as a neutral white pigment and a shading agent such as a black pigment or complement of the hue. By adding these agents to a common hue in varying proportions, a vast number of tints and shades of the hue quite beyond the limits of practicability of illustration by chips upon a chart of conventional arrangement can be formulated.

In order to match intermediate colors not shown by chips on a conventional color chart, it has been common practice to add tinting or shading agents slowly in small amounts, observe the elfect upon the color and repeat the operation, approaching the desired shade or tint gradually by guess work. Often the amount of added pigment was in excess of required to attain the desired match, in which instance, it was necessary then to add the other component (black or white) of the tinting or shading materials in order to compensate for the excess. Often the attainment of the desired gray value of a selected hue was a very tedious and time consuming operation requiring the employment for long periods of time of a highly skilled and experienced colorist.

This invention comprises the provision of a color chart of a hue comprising an odd number of chips showing a series of gray values of varying saturation arranged along an arc of a circle so that said values progressively vary in uniform increments from one end of the arc to the other. As a further feature, the invention comprises arranging a series of an odd number of such arcs of progressively increasing diameter concentrically about a central chip of the hue so that chips of like gray value on all of the 'ice arcs lie along common radii and the saturation of the chips from one are to the next vary in uniform increments. The inner chip which gives the hue may be regarded as constituting a circle. In that event, an outer arc of gray values obtained by mixing white and black alone or white and the complement of the hue in uniformly increasing increments corresponding to the gray values of the chips of the hue are added. At one end of this are is disposed a chip of the selected white and at the other end is disposed a chip of the black or of the complement of the hue. These chips are disposed upon radii at the extremities of the arcs and the chips thereupon give respectively tints and shades of the hue.

On this chart a color can be quickly and systematically compared to obtain the closest proximation thereof available on the chips of the chart. If it is of some intermediate value not represented by a chip, its composition in terms of amounts of spectral hue, tinting agent and graying agent can quickly be calculated merely by adding together the components of two neighboring chips upon opposite sides of the desired color. These neighboring chips may be located either on the common are representing variations of gray value of a predetermined saturation or on a common radius representing saturation values of colors of common gray value.

In event that the new color does not match the desired color sufiiciently closely, the addition of the components of said new color to the color of the chip immediately upon either side of the color will result in the desired color or will give a second new color. The color being sought will lie very close between the two new colors. By adding the twonew colors this desired color can be obtained or nearly obtained. If desired, a still closer approach to the selected color can be attained by adding together the components of the two new colors last found until a match is reached.

For a better understanding of the principles of the invention, reference may now be had to the accompanying drawings in which:

Fig. 1 is a view of a color chart constructed in accordance with the provisions of the invention; and

Fig. 2 is a view of a second, but related chart illustrating the use of the complement of the hue as a graying agent.

In the embodiment of the invention as shown in Fig. 1, the central color chip It} is of a hue or pure color such as a spectral hue or color. A card will be provided for each of these. In the embodiment of the invention as shown, equally spaced arcs as indicated at H are struck concentrically around the hue chip. The arcs are indicated as being semicircles or degrees, but it is obvious that the angles subtended thereby may be of any other convenient magnitude. The arcs are indicated as being divided into equal segments by an odd number of radii (12, 12a, 12b, 120, etc.). The outermost are 11h may be termed the gray value line. At the intersection of the extremity of this are and one of the outermost radii is indicated a chip CWh representing the color of a tinting agent such asa pure white or nearly pure White pigment. At the corresponding extremities of the intermediate arcs are chips representing the colors of tints of the hue as obtained by mixing the hue color with varying amounts of the white coloring matter or pigments. The amounts of the white in the color represented by the chips along the extreme radius 12h increases in uniform increments starting with the central hue chip It The total number of chips including the central hue chip along this radius. may be varied through substantially any number within. the limits of practicality though the number of the intermediate chips should always be odd. In the drawings, this number is nine but could be higher or lower if desired. The .number of the intermediate chips of course corre- 3 sponds to the number of the intermediate concentric arcs about the hue chip 10.

In like manner, at the other extremities of the arcs are disposed a series of chips CS, CSa, CSb, CSc, CSd, CSe and CS1, representing thecolors obtained by shading the hue color with black. The outermost chip CBh in this series may be the color value of a black pigment such as lamp black.

The intermediate chips between the chip 110 and the black chip CBlz represent intermediate shades of the hue which vary in equal increments outwardly, the strength of the hue becoming less and less away from hue chip 1t) and the black chip CBh being regarded as neutral or substantially so.

Along the outermost are 1171 previously mentioned as the gray value line are distributed equally spaced chips CG representing gray values obtained by mixing the white represented by the tinting color of chip CWh with the black of chip CB]: representing the graying color. The proportions of the black and the white are so chosen as to be represented by equal segments of the outermost arc, that is, the angles subtended by the radii between the central hue chip and the outermost gray value chips are equal. It is necessary that the number of the gray value chips between the black and the white be an odd number though which this limitation, substantially any number within the limits of practicality may be selected. For purposes of illustration, the number is indicated as fifteen. The are is thus divided by the chips disposed there along into sixteen spaces each of which represents 11 /4 degrees.

The intermediate arcs may be provided with the same number of chips as the outermost are though for purposes of simplifying the drawings, the number of the chips on the intermediate arcs are indicated as being but half of the number upon the outermost arc, the chips on the intermediate arcs being spaced by angles twice as great as those between contiguous chips upon the outermost are. This spacing, of course, may be varied at will so long as the total number of chips upon any given intermediate arc constitutes an uneven number. If desired a plurality of the outermost arcs may be provided with chips corresponding to the intermediate chips upon the outer arc. The chips being omitted from the inner arcs where the lineal distance between contiguous radii from the center of the arcs is relatively small. This avoids excessive crowding of the chips around the hue chip. The gray value for any particular color on any given arc not represented by a chip can readily be calculated by the methods already described by reference to the color of two chips disposed at equal distance from the space for the color not represented by a chip.

It will be observed that each of the chips is accompanied by indicia comprising the letters H, W and B, together with figures. The letter H indicates hue as indicated on the chip 10. The letter W indicates white that constitutes the tinting component represented by chip CWh which is added to the hue in order to lighten it. The letter B designates the black component as indicated by the chip CBlz'. This constitutes the graying agent. The numerals designate the number of units of the color which are incorporated into the mixture to obtain the desired value. For example, considering the chip at the intersection of arc 11d and the radius 12b designated as value, it will be observed that it is indicated as 6H+3W+6B. This means that the color is made up of 6 units of the hue, plus 3 units of white, plus 6 units of black. Again considering the third chip inwardly on the radius designated as value, it will be observed that it is indicated as being 5H+6W+4B. This of course means that the color of the chip is made up by mixing 5 units of hue, 6 units of white and 4 units of black.

Considering the middle radius indicated as /6 value, it will be observed that all of the colors contain equal amounts of white and black but the color of the chip contains decreasing proportions of the hue from the center outwardly.

It will be observed that on any given radius the ratio between the tinting agent and the graying agent remain constant on all of the chips, the proportion of the hue being variable. For example, considering the radius at /3 value it will be observed that the ratio of white to black is in all instances 1 to 3. On the ratius designated as A value the ratio is 1 to 2. The ratio for all of the other values is constant from the innermost to the outermost chip.

It will be apparent that the user of the chart can make up colors corresponding to any chip on the chart merely by adding together the three components, hue, white and black, in the amounts indicated by the indicia accompanying the chip. Assuming, however, that the user wishes to make up a color which is approximately half way between two chips on a given are, for example half way between the fourth chip inwardly on the radii representing value and /8 value, it will be observed that the neighboring chips are respectively 6H+3W+6B and 8H+3W+9B. Adding these two compositions together as follows:

it will be found that the desired composition is l4H+6W+15B. If the hue, the white and the black are mixed in these proportions the intermediate value is obtained. Assuming that the color obtained is still not quite what is desired, but lies for example between the newly found value and the chip 6H+3W+6B, the foregoing operation can be repeated as follows:

The new composition is 20H+9W+21B. Should it be decided that the desired color lies between the two newly found values the foregoing operation can be repeated. However, this probably seldom is necessary except in those instances Where possibly the color chart is provided with a relatively small number of chips.

Obviously the desired intermediate colors can be derived by mixing two colors equally distant along the arcs between radii 12 and 12/1 from the desired color on the are or it can be made up by appropriately proportioning the three basic colors, hue, black and white, making the simple additions above described. For example, suppose it is desired to derive the color 2H+2W+2B on the radius 12d and are 11 representing /2 value and that the two chips representing colors 2H+2W+6B on the shade side and the color 4H+6W+2B on the tint side are available. Adding these two together as follows:

the value 8H+8W+8B is obtained. Since 4 is a common factor, it can be canceled out leaving 2H+2W+2B or H+W+B which is the desired value as represented by the chip.

It will now be assumed that the two colors.represented by the chip l0H+6W+9B on the /8 value radius and the color represented by the chip 8H+3W+9B on the 78 value radius (12a) are available. Adding these two together it will be found that the sum is as follows:

Since 12H+6H+12B contains the common factor 3, the latter may be canceled out leaving 6H+3W+6B as the desired value of the chip on the radius 5 value.

The saturation value on the chips on a given radius are also, as previously indicated, separated by equal increments starting from the hue and extending outwardly to the gray value. Assuming that a chip of desired saturation value on a given radius is not available, it is therefore possible to add two colors equally spaced from the desired to obtain a color having the desired saturation and value. Suppose for example, that it is desired to determine the composition of the color represented by the chip on are 110 and radius 12 while the composition colors represented by the two contiguous 'chips (3H+2W+B and 3H+4W+2B) are available.

The desired color may then be derived by adding together in equal amounts the two colors as follows:

By mixing hue, black and white in the above proportions, the desired color'is derived. This provides a convenient method of determining the components desired for obtaining any predetermined saturation and value and for moving inwardly or outwardly along any given axis. Obviously, having arrived at a desired saturation and value, it becomes possible to move as desired with the newly derived color along the arcs representing gray values 11a, 11b, 11c, 11d, lle, 11] and 11g.

To make up the chart, the three basic colors, hue, black and white are selected. It usually is preferred that these be mixed with a liquid vehicle, though the use of dry pigment is included within the scope of the invention. The amount of vehicle in the white is selected to give a composition of good hiding power and to insure that the resultant composition can be readily blended with the other components. The color of this composition provides chip CWh. The amount of vehicle added to the hue chip H is so chosen as to provide a definite tinting strength which has been found to be satisfactory and which assures a reasonably uniform gradient of tint along the radius 12h as the hue is added to the white in increasing amounts from the chip CWh inwardly toward the hue chip. Usually conventional tinting strength is satisfactory. The concentration of the black in the vehicle is also similarly chosen so that the gradient in gray value of the chip between the chips CWh and CBh is smooth and uniform as the selected volumes of black are incorporated with the white.

In order to establish the middle or /2 gray value on the arc 11h, equal volumes of the white and the black are mixed. This gives the gray value chip CGc at the intersection of the arc 11h and the middle radius 12d. The composition of the color of this chip therefore is B+W. This ratio of 1 to 1 between the black and the white is carried by all chips upon the radius 12d. In other words, all chips on this radius will have an equal amount of white and black but will vary in saturation by reason of the addition of varying amounts of hue.

Having established the gray value at the middle point of the arc 11h, one is now in a position to determine the gray value on the midportion of the sector in between the radius 12 and the intermediate radius 12b. This is readily obtained by adding together equal quantities of the original black composition represented by the chip CBh and the color of the intermediate chip just found, the latter being designated as CGd. The intermediate value on the radius 12b half way between the radius 1 12b and 12 may be termed value and is of the composition W+2B. The ratio (1 to 2)- between white and black is also carried in all of the colors on the radius 12!). By using the newly found gray values along the arc 11a, adding them either to each other or to the original black or to the gray of the /2 value the sector of the arc to the right of the intermediate arc 12b can be divided into any appropriate number of subdivisions though, of course, it is desirable that the number of radii established be odd.

It is evident that the gray values added together to determine intermediate values are equally distant from the gray value to be determined. The gray values to the left of the radius 110? are established in like manner first by mixing equal volumes of white and the color of the gray value on the radius 11d. This establishes value which in terms of quantities of black and white is 2W+B. The two sectors of the are as thus established, each representing degrees, may then be divided into as many subdivisions as desired by adding together newly found values or newly found values and the white of chip CWh which are equally distant on the arc 11h from the desired value.

The shades of the hue represented by the chips CSa through CSg on the radius 12 can be determined by a similar process of interpolation adding together quantities of the hue composition and the black composition. The middle chip of this series is determined by adding to equal quantities of white and black a quantity of hue equal to the sum of the two and therefore is of the composition 2H+W+B and is represented as CSd. The remainder of the radius is again broken down into two equal sections by adding the composition of CSd to CGh to determine the intermediate composition CS which is 2H+2W+2B or by adding the composition of CSd, ZH-I-W-l-B, H+H to obtain the intermediate value 4H+W+B. This operation can be repeated as often as desired in order to break down the radius 120! into as many sections as desired. The values or shades of the chips as thus established are distributed at equal distances along the radius 12d and establish the radius of the intermediate are between. the central hue chip and the arc of the gray values.

A tinting scale is made up along the radius 12h in the same manner as the shading scale on the radius 12. The chips representing tint'are disposed at the opposite ends of the arcs from the chips representing shades. It is to be understood that the intermediate colors on any of the arcs between the shade axis or radius and the tint radius can be determined in similar manner by adding together the quantities of the hue and the black represented by the chip at one end of the arc and the hue and the white represented by the chip at the other end of the same are to establish the composition of the color represented by the corresponding chip on the intermediate radius 12d and then breaking up the two segments to the right and the left of the intermediate radius 12d in the manner already described for the gray value.

It is also feasible to calculate the color values along any radius when any color on the radius is known. By way of illustration it will be assumed that the new color to be found is between that of the center or hue chip and that of the known chip. The color on the radius midway between the hue chip and the known color is found by the summation of the amount of the black (B) and white (W) in the known chip. An amount of hue equal to the numerical sum is then added to the amount of hue of the known chip. This gives the composition of the color midway between the known chip and the hue chip. By repetitions of this operation, or by adding the components of neighboring colors on a common radius, it is possible to derive or closely to approach any color between the known chip and the hue chip. The following example illustrates the determination of a color by this method. The known color will be assumed to be 4H+2W+6B upon the radius 121;. The color midway between it and the hue is 4H+2H+6H+2W+6B, or 12H+2W+6B, which is the desired value. The latter value, of course, can be used further to subdivide the radius using the techniquesdescribed. This method can be-used to subdivide the radius into as small segments as desired to approach any selected color between the known color and the hue-chip.

A color midway between'thegray value on the gray value are and a known color on a given radius, e. g. the radius 12b, can be found by adding to the sum of the colors of the known chip (hue, black and white), black and white in an amount equal to the black and white in the corresponding gray value on the gray value line or are 1-1/1. For example, suppose that the color 3H+W+2B on the radius 12b is known. The color midway between the known color and the corresponding gray value is 3H+W+2B+VJ+2B or 3H+2W+4B. By using these newly determined values, a given radius may be divided into as many segments asdesired and thecorresponding color chips can be applied at the appropriate places. For example, assuming that the color 3H+W+ 2B on the radius 12b is known, the median color between it and the hue is 3H+H+2H+W+2B or 6H+ W-i-ZB. The median color between that of the chip of the composition 3H+W+2B on the same radius and the value W+2B on the gray value arc is 3H+W+2B+W+ 2B or 3H+2W+4B. The color intermediate of that of the chip 3H+W+2B and the new found color 3H+2W+ 4B is:

Of course the common factor 3 could be eliminated, if desired to leave 2H+W+2B. Since the ratios of the color components to each other are the same, this operation is optional.

The determination of intermediate colors has been illustrated by instances in which the color to be found was already determined and shown on the chart. This was merely for purposes of providing check answer of the determination made. It will be apparent that color chips of which are not shown upon the chart, but being intermediate of the colors already known and shown can be found in precisely the same way by adding the colors of the contiguous chips to each other.

In the foregoing embodiment of the invention, graying was effected by addition of black to white to obtain the desired gray values which, with the hue in appropriate amount, gave the desired color. It is to be understood that the complementary color of the hue may be substituted for the black to obtain a neutral color. This is commonly known as graying with the complement; The chart as given in Fig. 2 illustrates such method. Red may be selected as a representative hue and it complement is green. However, any other hue might be selected. Needless to say, the hue and complement may be reversed in position. For example, green may be placed on the central chip. Then, e. g. red is placed in the position of black.

In the chart shown by Fig. 2, the tint scale is indicated :as being upon a radius 20 from a hue chip 21. This chip may be of a specular color selected from a conventional color wheel. The chip 21a at the outer extremity is white. The scale on the radius 20 may be the same as the tint scale 1211 in Fig. l. The tint chips along the radius are established in the manner as already described in connection with Fig. l by mixing equal amounts of hue and white to find the median tint 21b and then subdividing the segments of the radius. These tint chips establish radii for concentric arcs 22 that correspond to the arcs in Fig. l. The arcs at their opposite extremities intersect radius 23 and shade chips are disposed along this radius to provide a scale of shades of the hue. The intermediate chips are indicated at 24. The outermost chip 26 on the radius is of the complement of'the hue.

To make up the color components which are to' be mixedcoloring materials (hue, white and complement) are separately mixed with a vehicle in suchamounts that the addition of the hue stepwise to the white in the manner already indicated gives a relatively uniform gradation of tints from the pure color to the white on the tint scale. The complement is also mixed with vehicle in such manner that a smooth gradation of tints of the complement will result as the complement is added to white along the outer arc, to establishvalues. Shade values are established on the shade scale by adding complement to the hue.

To make up the value scale on the outermost arc equal volumes of white and complement are mixed to establish /2 value which falls on the mid point of the arc, the process employed to establish the gray value scale on are 1111 of Fig. l is repeated for the intermediate values.

To establish a shade scale on the radius 23 equal volumes of hue and complement are mixed to give a color falling on the intersection of the mid one of the arcs and the radius. If the hue and the complement have been diluted with vehicle in proper amounts, this will give the neutral value. The resultant chip is indicated as 27. The chips on the radius 2?: beyond the chip 27 progressively increase in color of the complement and naturally on the side toward the hue chip, they progressively increase in the color of the hue. The technique of establishing the intermediate colors in various areas of the chart as given for Fig. 1 are repeated. The addition of the components of the colors of two chips which on either an arc or a radius have been established, gives a color halfway between the two established colors. Colors as thus found can be employed in the formation of still other colors on the chart thus to fill out the latter. For example, assuming it is desired to find a color on the radius of value, e. g. the median color midway of the radius, the color of. one half value indicated as 2H+W+C may be added to the shade H-l-C on the same are, where H, W and C designate respectively hue, white and complement. The computation is as folows:

Assuming it i desired to find a color, e. g. the color on the same arc, but on the radius of /8 value, the computation involves addition of the colors on each side as follows:

which is the desired color.

In the interests of simplicity, the compositions of the colors of only a few representative chips on the chart of Fig. 2 have been applied. Others can be computed by repetition of the foregoing operations or by reference to the compositions for the colors of the chips in corresponding positions on the chart of Fig. 1. In the latter, the shading agent (black) is replaced by a like amount of complement (C).

Colors not actually illustrated on the chart by ch1ps can be determined by adding together the compos1t10n of two known neighboring colors on a radius or on an are as may be convenient. If the desired color is midway between the two known colors of the chart, the desired color is found in a single step, but if it is not midway, the components of the newly determined color can be added to the components of one of the known colors closest to effect a still closer approach to the desired value. These techniques are the sameas those already. described 1n connection with Fig. l. u

The chart, when complete, will in effect compnse an inner semicircle and an outer arcuate band, the semicircle being dominated by the hue and the bandv being dominated by the complement. Between the two is a median arc-of neutral value and shading from the darkest neutral value at the shade end and gradually becoming paler tints toward the other end of the arc. The neutral arc terminates on the radius 20 on a chip 21b which is the median tint of the hue.

It will be manifest that the codes giving the amounts of the components required to give a color of a chip on the charts of Fig. 1 or 2 may be replaced by arbitrary designations such as letters, numbers or names. The compositions corresponding to such designations may then be separately tabulated for convenient reference.

I claim:

1. A chart of tints and shades of a selected hue for use in matching and compounding colors which are mixtures of said hue with a tinting and a shading agent, comprising a sheet member having a color chip of the hue selected, chips of the tints and shades of the hue arranged in a series of arcs of circles with the chip of the hue as a center, chips on a given are being of the same degree of saturation, there being an uneven number of arcs counting the chip of the hue as one and there being an uneven number of chips on the arcs, chips on a given are being arranged from one end of the arc in the order of depth of shade, chips of the same gray value being disposed upon a common radius and the arcs being equally spaced and being arranged in a series in which the saturation of the chips is inversely proportional to the distance from the center, the chips upon each are being spaced an increment from their neighbors on the are proportional to the difference in gray value between a chip and its nearest neighbor and indicia associated with the chips whereby the amount of tinting and graying material required to be added to the hue to arrive at the value of a selected color can be ascertained.

2. A color chart of tints and shades of a selected hue comprising a sheet member having a color chip of the selected hue and chips of tints and shades of the hue arranged in a series of arcs of circles with the first mentioned chip as a center, there being an uneven number of arcs counting the selected chip as 1 and there being an uneven number of chips on each of the arcs, the chips on a given are being arranged from one end of the arc in the order of their gray value, chips of the same gray value being disposed upon a common radius, the arcs being equally spaced and being arranged in a series in which the saturation of the chips is inversely proportional to the distance from the center, and indicia associated with the chips whereby the amounts of tinting and shading materials required to be added to the hue on the chart to arrive at a selected color can be ascertained.

3. A color chart comprising a sheet member having an outer arc indicated thereupon, the are having a hue chip as a center and having a chip of a selected neutral white at one end and a chip of selected neutral graying material at the other and a series of an uneven number of chips of neutral gray between the end chips, the gray chips being uniformly graduated in gray value from one end to the other, and a series of an uneven number of intermediate arcs concentric with the first arc, a series of chips of tints and shades of the selected hue arranged upon each of the intermediate arcs, the angles between the chips on each are being equal to the angles between the neutral gray chips on the outer arc, the gray value from chip to chip along a given arc being equal to the neutral gray value of the outer arc and the saturation of a given chip upon an are being inversely proportional to the distance of the chip from the center of the arc and indicia associated with the chips whereby the amounts of hue imparting material, tinting material and graying material required for the color of each chip can be selected.

4. A color chart of tints and shades of a hue comprising a sheet member having-a chip of the hue color thereupon, a pair of radii divergent from said chip and chips of tints and shades of the hue arranged in scales respectively of tints and shades upon the radii, a middle tint chip at the midpoint of the tint scale comprising hue with an equal amount of white admixed, a chip midway between the middle chip and the hue chip comprising the color of the middle chip but with the hue doubled and a chip midway between the middle chip and white which is the same in color as the middle chip but with the white doubled, the scale of shades being made up in the same way as the scale of tints but with the graying agent replacing white, the chips on the tint scale and the corresponding tints on the shade scale being connected by arcs of chips having gray values progressively increasing from the tint scale to the shade scale, the colors in the middle of the arcs comprising equal amounts of white and graying agent and the color of a chip midway on an arc between the chip at the middle of the arc and the tint scale and shade scale being the sums of the colors of the chips of the middle of the arcs and respectively the tint and shade dependent upon which side of arc the chip is disposed upon.

5. A chart as defined in claim 4 comprising chips along the arcs and being midway between the chips already described, these latter chips being of composition corresponding to the sum of the same components of the contiguous chips u'pon opposite sides thereof along the arc.

6. A chart as defined in claim 4 in which the graying agent is a complement of the hue.

7. A chart as defined in claim 5 in which the graying agent is a complement of the hue.

References Cited in the file of this patent UNITED STATES PATENTS OTHER REFERENCES Color Science by William Ostwald, 2 vols., Plates 1, 3 and 4 in Part I, Plate 2 in Part H. Also pp. 106113. 

